"Russian children's music, that's what's playing in our house these days," said Cooper, who welcomed his little girl, Lea De Seine, with his girlfriend, Russian supermodel Irina Shayk, in March 2017.

"So I am singing along to that quite often," Cooper added, adorably.

Before coming home to sing his little girl some soothing Russian lullabies on Monday, Cooper and his co-star, Lady Gaga, dressed to the nines for their big red carpet premiere, and couldn't have looked classier outside the storied Shrine.

"I really wanted [the premiere] to be here," Cooper shared. "It just always felt like this was the place to have it."

Three of the scenes in the film were shot at the Shrine Auditorium, and the historic venue's storied stage showcased several performances by Judy Garland -- who famously starred in Gaga's role in the 1954 iteration of A Star Is Born.

"We have so many people [here] that worked on a movie, all the people that were extras, a lot of the crew. So it's really a special night for all of us to be together and watch the movie," Cooper shared.

The actor also opened up about some of the film's key casting choices -- especially those roles who went to people Cooper knows personally.

"There's a lot of real-life people [in the movie]. My ear doctor is the ear doctor, half the crew is in the movie, a lot of my friends from grad school," Cooper shared. "That's the best thing about being able to make a movie is you get to cast the movie."

Another role that went to someone he's close to was that of his character's canine companion, played by Cooper's real-life beloved dog, Charlie.

Speaking with Gaga later on the red carpet, the actress couldn't contain her excitement over getting to spend time on set with the precious pooch, telling ET, "We were always playing with Charlie!"